Anisotropic diffusion at the field scale in a 4-year multi-tracer diffusion and retention experiment – I: Insights from the experimental data

Abstract Claystones are considered worldwide as barrier materials for nuclear waste repositories. In the Mont Terri underground research laboratory (URL), a nearly 4-year diffusion and retention (DR) experiment has been performed in Opalinus Clay. It aimed at (1) obtaining data at larger space and time scales than in laboratory experiments and (2) under relevant in situ conditions with respect to pore water chemistry and mechanical stress, (3) quantifying the anisotropy of in situ diffusion, and (4) exploring possible effects of a borehole-disturbed zone. The experiment included two tracer injection intervals in a borehole perpendicular to bedding, through which traced artificial pore water (APW) was circulated, and a pressure monitoring interval. The APW was spiked with neutral tracers (HTO, HDO, H2O-18), anions (Br, I, SeO4), and cations (Na-22, Ba-133, Sr-85, Cs-137, Co-60, Eu-152, stable Cs, and stable Eu). Most tracers were added at the beginning, some were added at a later stage. The hydraulic pressure in the injection intervals was adjusted according to the measured value in the pressure monitoring interval to ensure transport by diffusion only. Concentration time-series in the APW within the borehole intervals were obtained, as well as 2D concentration distributions in the rock at the end of the experiment after overcoring and subsampling which resulted in �250 samples and �1300 analyses. As expected, HTO diffused the furthest into the rock, followed by the anions (Br, I, SeO4) and by the cationic sorbing tracers (Na-22, Ba-133, Cs, Cs-137, Co-60, Eu-152). The diffusion of SeO4 was slower than that of Br or I, approximately proportional to the ratio of their diffusion coefficients in water. Ba-133 diffused only into �0.1 m during the �4 a. Stable Cs, added at a higher concentration than Cs-137, diffused further into the rock than Cs-137, consistent with a non-linear sorption behavior. The rock properties (e.g., water contents) were rather homogeneous at the centimeter scale, with no evidence of a borehole-disturbed zone. In situ anisotropy ratios for diffusion, derived for the first time directly from field data, are larger for HTO and Na-22 (�5) than for anions (�3�4 for Br and I). The lower ionic strength of the pore water at this location (�0.22 M) as compared to locations of earlier experiments in the Mont Terri URL (�0.39 M) had no notable effect on the anion accessible pore fraction for Cl, Br, and I: the value of 0.55 is within the range of earlier data. Detailed transport simulations involving different codes will be presented in a companion paper.

Numerical simulation of anomalous diffusion with application to medical imaging

The first objective of this project is to develop new efficient numerical methods and supporting error and convergence analysis for solving fractional partial differential equations to study anomalous diffusion in biological tissue such as the human brain. The second objective is to develop a new efficient fractional differential-based approach for texture enhancement in image processing. The results of the thesis highlight that the fractional order analysis captured important features of nuclear magnetic resonance (NMR) relaxation and can be used to improve the quality of medical imaging.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.

A model for doped-oxide-source diffusion with a chemical reaction at the silicon-silicon dioxide interface

A mathematical model for doped-oxide-source diffusion is proposed. In this model the concept of segregation of impurity at the silicon-silicon dioxide is used and also a constant of “rate limitation” is introduced through a chemical reaction at the interface.

Ocular Reconstruction After Zygomatic Complex Fracture With Retention of a Foreign Body

Facial injuries with the retention of foreign bodies inside the tissues, both in soft and hard ones, can cause major functional and aesthetic damage. Among the different etiological agents, cutting tools, fragments of a firearm, the splinter of wood, steel, or iron, launched by misuse, or even caused by defects in equipment, are the main cause of these injuries. The aim of this study was to discuss the peculiarity of the multidisciplinary approach in caring of a 33-year-old man, victim of an accident at work, by the rupture of an emery disc and consequent penetration of the fragments in violation of the tissues in the orbital and zygomatic region of the left side, with perforation of the eyeball and orbital-zygomatic fracture. Urgent treatment consisted of debridement of wounds, bleeding control, removal of foreign bodies, fracture reduction with rigid internal fixation, and suture, performed by the oral and maxillofacial surgical team. Reconstruction of orbital tissues by the ophthalmology team consisted of suture of the injuries. About 1 month after the trauma, phthisis bulbi was noted, and the patient underwent a new procedure under general anesthesia for eye evisceration and installation of an alloplastic prosthesis associated with the homogenous sclera. Facial harmony was restored, especially in aesthetics and function of the zygomatic-orbital complex.

Weakly anomalous diffusion with non-Gaussian propagators

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H approximate to 1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H = 1/2 but with a non-Gaussian propagator.

Partial reconstruction of the trajectories of a discretely observed branching diffusion with immigration and an application to inference

In this treatise we consider finite systems of branching particles where the particles move independently of each other according to d-dimensional diffusions. Particles are killed at a position dependent rate, leaving at their death position a random number of descendants according to a position dependent reproduction law. In addition particles immigrate at constant rate (one immigrant per immigration time). A process with above properties is called a branching diffusion withimmigration (BDI). In the first part we present the model in detail and discuss the properties of the BDI under our basic assumptions. In the second part we consider the problem of reconstruction of the trajectory of a BDI from discrete observations. We observe positions of the particles at discrete times; in particular we assume that we have no information about the pedigree of the particles. A natural question arises if we want to apply statistical procedures on the discrete observations: How can we find couples of particle positions which belong to the same particle? We give an easy to implement 'reconstruction scheme' which allows us to redraw or 'reconstruct' parts of the trajectory of the BDI with high accuracy. Moreover asymptotically the whole path can be reconstructed. Further we present simulations which show that our partial reconstruction rule is tractable in practice. In the third part we study how the partial reconstruction rule fits into statistical applications. As an extensive example we present a nonparametric estimator for the diffusion coefficient of a BDI where the particles move according to one-dimensional diffusions. This estimator is based on the Nadaraya-Watson estimator for the diffusion coefficient of one-dimensional diffusions and it uses the partial reconstruction rule developed in the second part above. We are able to prove a rate of convergence of this estimator and finally we present simulations which show that the estimator works well even if we leave our set of assumptions.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.

Highly stereoselective decarboxylation of (+)-1-Bromo-1-chloro-2,2,2-trifluoropropanoic acid gives (+)-1-Bromo-1-chloro-2,2,2-trifluoroethane ((+)-Halothane) with retention of configuration

The absolute configuration of the title acid (2) has been determined to be S by X-ray crystallography. Thus, decarboxylation of 2 produces (S)-(+)-halothane with 99% retention of configuration. This behavior is compared to other stereoselective decarboxylation reactions of ?-haloacids from the literature that also give high degrees of retention of configuration when in the form of their quaternary ammonium salts, which contain one proton. The proton of the ammonium salt is necessary to protonate the anionic intermediate formed from decarboxylation. In the absence of this relatively acidic proton, we had previously found that using triethylene glycol (TEG) as both solvent and proton source for the decarboxylation reaction of acid 2 caused poor stereoselectivity. This was in contrast to 1,2,2,2-tetrafluoro-1-methoxypropionic acid (6), which showed a high degree of retention of configuration in TEG. To rationalize this differing behavior we report DFT studies at PCM-B3LYP/6-31++G** level of theory (the results were additionally confirmed with 6-311++G** and aug-cc-pVDZ basis sets). The energy barrier to inversion of configuration of the anionic reaction intermediate of acid 2 (11) is 10.23 kcal/mol. However, we find that the anionic intermediate from acid 6 (10) would rather undergo ?-elimination instead of inversion of configuration. Thus the planar transition state required for inversion of configuration is never reached, regardless of the rate of proton transfer to the anion.

Fipronil insecticide: Novel photochemical desulfinylation with retention of neurotoxicity

Fipronil is an outstanding new insecticide for crop protection with good selectivity between insects and mammals. The insecticidal action involves blocking the γ-aminobutyric acid-gated chloride channel with much greater sensitivity of this target in insects than in mammals. Fipronil contains a trifluoromethylsulfinyl moiety that is unique among the agrochemicals and therefore presumably important in its outstanding performance. We find that this substituent unexpectedly undergoes a novel and facile photoextrusion reaction on plants upon exposure to sunlight, yielding the corresponding trifluoromethylpyrazole, i.e., the desulfinyl derivative. The persistence of this photoproduct and its high neuroactivity, resulting from blocking the γ-aminobutyric acid-gated chloride channel, suggest that it may be a significant contributor to the effectiveness of fipronil. In addition, desulfinylfipronil is not a metabolite in mammals, so the safety evaluations must take into account not only the parent compound but also this completely new environmental product.